An electrical circuit may include hundreds of, or even more components, devices, modules, dies, etc., connected by metal traces, vias, solder bumps, etc. With the increasing scale of the electrical circuit, and the increasing complexity, it is very difficult, or even impossible, to completely rely on a human being to design an electrical circuit or to build a “test” circuit before an actual circuit is put into mass production. Circuit simulation based on computer-aided design has become an important tool for electrical circuit designers.
The behavior of an electrical circuit may depend on various parameters and may comprise multiple variables. Often time, the simulation may need to be “simplified,” focusing on some of the parameters and variables. Traditional circuit simulation methods usually pay much attention to the models describing the distributions of electric current density and electric potential. In such models, many other parameters, such as temperature, are set with a constant value.
The traditional circuit simulation methods as described above may provide acceptable results for older generations of circuits where, for example, the circuit density is not large and the operation frequency is not high. For such circuits, the design margin is large enough to absorb the deficiencies caused by an inaccurate design. However, with the development of integrated circuit technology, the circuit density and the data rate of a circuit have increased, the data transition time has reduced, and the voltage and timing margins have also been reduced. Due to the shrinking in the design margin, more accurate design is needed.
Generally, temperature is one of the parameters that can affect the performance of the electrical circuit. For example, the resistance of the traces in the circuit may be temperature dependent. There is a need for a circuit simulation method and apparatus that takes into consideration both the electric and thermal characteristics of an electrical circuit.